I have a retweet bot that I created in PHP using oAuth that I’m using to retweet the statuses from list members. The bot works well for a while and then starts getting 403 error messages. I assume I’m breaking some rate limit. My question is, how do I find out what rate limit I’m breaking and throttle my bot in a way that stays within the limits?

You should take a look at the automation rules if you are building this kind of app.

You can check your current rate limit status for the read endpoints by checking the X-Rate-Limit HTTP headers. For post / create operations, the limits are account-based, and are listed on the support pages.

It seems likely that you’re hitting an account limit, not an API rate limit - I assume this is failing when you try to retweet?